臺灣博碩士論文加值系統

本論文針對TE極化波入射的情況下,對於非完全導體的電磁成像問題進行探討。
對於非完全導體而言，我們利用非完全導體表面阻抗的觀念再加上表面電流的觀念，在物體的邊界上，可導出非線性積分方程式，繼而利用動差法求得正散射公式。經由推導出的正散射公式，我們可以得到散射場的相關資料。在於逆散射部分，我們使用了基因法則(Genetic Algorithm)，經由適當地選取參數，同時結合所推導的散射公式，我們可以由觀測點所測得的散射場值，經由基因法則的運算，來反求得物體的形狀函數。
就整體而言不論初始的猜測值如何，基因法則總會收歛到整體的極值(global extreme)，因此，在數值模擬中，即使最初的猜測值與實際值相距甚遠，我們仍可求得準確的數值解，成功的重建出物體形狀函數與導電率。而且量測的散射場即使加入高斯分佈的雜訊存在，依然可以得到良好的重建結果。此外我們也對於形狀函數跟導電率的雜訊容忍量予以比較。

This paper presents a computational approach to the transverse electric (TE) wave imaging of an imperfectly conducting cylinder. An imperfectly conducting cylinder of unknown shape and conductivity scatters the incident wave in the free space, and the scattered field is recorded outside the object. Based on the boundary condition and measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization one that solved by Genetic Algorithm. Numerical results demonstrated that, the even when the initial guess is far away from the exact one, good reconstruction for shape and conductivity of the object can be obtained and the object’s conductivity also can be reconstruction excellent, In addition, the effect of noise is also be investigated.

第一章 簡介...................................1
1.1 研究動機與相關文獻....................... 1
1.2 本研究之貢獻............................. 5
1.3 各章內容簡述............................. 5
第二章 非完全導體在自由空間之逆散射.......... 7
2.1 理論推導................................ 8
2.2 數值方式................................ 11
2.3 基因演算法之基本概念.................... 15
2.4 介紹基因演算法則中的運算方式............. 16
2.4.1 編碼與解碼............................ 16
2.4.2 基因法則三大運算法則.................. 19
2.4.3 基因法則的主要特性.................... 22
2.5 基因法則在逆散射的應用.................. 24
第三章 數值分析與模擬結果.................... 32
3.1 模擬環境介紹............................ 32
3.2 正散射之驗證............................ 33
3.3 二維兩瓣物體之重建結果.................. 33
3.4 二維三瓣物體之重建...................... 34
3.5 散射場雜訊對重建的影響.................. 34
3.6 兩瓣物體導電率可重建範圍................ 35
3.7 三瓣物體導電率可重建範圍................ 35
3.8 不同編碼參數之模擬...................... 36
第四章 結論.................................. 48
參考文獻..................................... 50
圖2. 1 模擬環境………………………………………………………28
圖2.2 差分電流密度與電荷密度分佈………………………………… 29
圖2.3 各點源與場點的關係………………………………………….. 30
圖2.4 基因法則流程圖…………………………………………………. 31
圖3.1 二維兩瓣物體還原結果…………………………………………. 37
圖3.2 兩瓣物體每代物體函數偏差量………………………………... 38
圖3.3 兩瓣物體每代導電率偏差量……………………………………. 39
圖3.4二維三瓣物體還原結果………………………………………….. 40
圖3.5三瓣物體每代物體函數偏差量………………………………….. 41
圖3.6 三瓣物體每代導電率偏差量……………………………………. 42
圖3.7 三瓣不同noise形狀偏差量與導電率偏差量…………………... 43
圖3.8 兩瓣物體各不同導電率的還原偏差……………………………. 44
圖3.9 三瓣物體各不同導電率的還原偏差……………………………. 45
圖3.10 24bit之每代物體函數估測結果………………………………... 46
圖3.11 24bit之每代導電率之估測結果………………………………... 47
表2. 1 基因演算法相關名詞解釋與中英對照表..............26

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